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{{Draft article}}

{{Condensed matter physics}}
{{Time sidebar |science}}
A '''time crystal''' or '''space-time crystal''' is a hypothetic structure that repeats periodic in time, as well in space. Normal three-dimensional [[Crystal|crystals]] have a repeating pattern in space, but remain unchanged with respect to time; time crystals repeat themselves in time as well, leading the crystal to change from moment to moment. A time crystal never reaches [[thermal equilibrium]] as it is a type of non-equilibrium matter - a form of matter proposed in 2012, and first observed in 2017.  This state of matter cannot be isolated from its environment - it is an open system in [[Non-equilibrium thermodynamics|non-equilibrium]].  

The idea of a time crystal was first described by [[Nobel laureate]] and [[MIT]] professor [[Frank Wilczek]] in 2012. Subsequent work developed a more precise definition for time crystals, ultimately leading to a proof that they cannot exist in equilibrium. Then in 2016, Norman Yao and colleagues at the [[University of California, Berkeley|Berkeley]] proposed a way to create non-equilibrium time crystals, which [[Christopher Monroe]] and [[Mikhail Lukin]] independently confirmed in their labs. Both experiments were published in ''[[Nature (journal)|Nature]]'' in 2017.

==History==
[[File:Frank Wilczek.jpg|thumb|[[Nobel laureate]] [[Frank Wilczek]] at [[University of Paris-Saclay]]]]
The idea of a space-time crystal was first put forward by [[Frank Wilczek]], a professor at [[MIT]] and [[Nobel laureate]], in 2012.<ref>See {{harvp|Wilczek|2012}} and {{harvp|Shapere|Wilczek|2012}}</ref>

Xiang Zhang, a nanoengineer at [[University of California, Berkeley]], and his team proposed creating a time crystal in the form of a constantly rotating ring of charged ions.<ref>See {{harvs|txt|last1=Li et al.|year1=2012a|year2=2012b}}, Wolchover 2013</ref>

In response to Wilczek and Zhang, Patrick Bruno, a theorist at the [[European Synchrotron Radiation Facility]] in [[Grenoble]], France, published several papers claiming to show that space-time crystals were impossible.<ref>See {{harvp|Bruno|2013a}} and {{harvp|Bruno|2013b}}</ref><ref>{{Harvp|Thomas|2013}}</ref>

Subsequent work developed more precise definitions of [[time translation symmetry]]-breaking which ultimately led to a 'no-go' proof that quantum time crystals in equilibrium are not possible.<ref>See {{harvp|Nozières|2013}}{{sfn|Yao et al.|2017|p=1}} and {{harvp|Volovik|2013}}{{sfn|Yao et al.|2017|p=1}}</ref><ref>See {{harvp|Watanabe|Oshikawa|2015}}</ref>

Several realizations of time crystals, which avoid the equilibrium no-go arguments, were later proposed.<ref>See {{harvp|Wilczek|2013b}} and {{harvp|Yoshii et al.|2015}}</ref> Krzysztof Sacha at [[Jagiellonian University]] in [[Krakow]] predicted the behaviour of discrete time crystals in a periodically driven many-body system.<ref>See {{harvp|Sacha|2015}}</ref> Work with spin systems<ref>See {{harvp|Khemani et al.|2016}} and {{harvp|Else et al.|2016}}</ref> suggested periodically driven quantum systems could show similar behavior.  And Norman Yao at [[University of California, Berkeley|Berkeley]] studied a different model of time crystals.<ref>See {{harvp|Yao et al.|2017}}, {{Harvp|Richerme|2017}} </ref>

Yao's blueprint was successfully used by two teams: a group led by [[Mikhail Lukin]] at [[Harvard university|Harvard]]<ref>See {{harvp|Choi et al.|2017}}</ref> and a group led by [[Christopher Monroe]] at [[University of Maryland]].<ref>See {{harvp|Zhang et al.|2017}}</ref> 

==Time translation symmetry==
{{main article|Time translation symmetry}}
Symmetries in nature lead directly to conservation laws, something which is precisely formulated by the [[Noether theorem]].{{sfn|Cao|2004|p=151}}

The basic idea of ''time-translation symmetry'' is that a translation in time has no effect on physical laws, i.e. that the laws of nature that apply today were the same in the past and will be the same in the future.{{sfn|Wilczek|2015|loc=chpt. 3}} This symmetry implies the [[conservation of energy]].{{sfn|Feng|Jin|2005|p=18}}

===Broken symmetry in normal crystals===
{{main article|Crystal symmetry|spontaneous symmetry breaking}}
[[Image:Phonon nu process.svg|thumb|right|250px|Figure 2. Normal process (N-process) and Umklapp process (U-process). While the N-process conserves total phonon momentum, the U-process changes phonon momentum.]] Normal crystals exhibit ''broken translation symmetry'':  they have repeated patterns in space, and are not invariant under arbitrary translations or rotations. The laws of physics are unchanged by arbitrary translations and rotations, but if we hold fixed the atoms of a crystal, the dynamics of electrons or other particles in the crystal depends on how it moves relative to the crystal, and particles' momentum can change by interacting with the atoms of a crystal—for example in [[Umklapp process]]es.{{sfn|Sólyom|2007|p=193}} [[Quasimomentum]]{{sfn|Sólyom|2007|p=191}}, however, is conserved in a perfect crystal.

===Broken symmetry in time crystals===
Time crystals seem to break ''time-translation symmetry,'' and have repeated patterns in time. Fields or particles may change their energy by interacting with a time crystal, just as they can change their momentum by interacting with a spatial crystal.

==Thermodynamics==
Because a time crystal is a driven (i.e., open) [[Open quantum system|quantum system]] that is in [[perpetual motion]], it does not violate the laws of thermodynamics:{{sfn|Chernodub|2013b|p=2, 13}} Energy is conserved, it does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual store of work.  But as long as it is driven by an outside force, it may change perpetually in with a fixed pattern in time.{{sfn|Chernodub|2013a|p=10}}  

It has been proven that a time crystal cannot exist in thermal equilibrium.  Recent years have seen more studies of non-equilibrium quantum fluctuations.<ref>See {{harvp|Esposito et al.|2009}} and {{harvp|Campisi et al.|2011}} for academic review articles on non-equilibrium quantum fluctuations</ref>

==Experiments==
In October 2016, Christopher Monroe at the [[University of Maryland, College Park|University of Maryland]], claimed to have created the world's first discrete time crystal. Using the idea from Yao's proposal, his team trapped a chain of [[Ytterbium-171|<sup>171</sup>Yb<sup>+</sup>]] ([[ytterbium]]) ions in a [[Paul trap]], confined by radio frequency electromagnetic fields. One of the two [[Spin quantum number|spin states]] was selected by a pair of laser beams. The lasers were pulsed, with the shape of the pulse controlled by an [[acousto-optic modulator]], using the [[Tukey window]] to avoid too much energy at the wrong optical frequency. The [[hyperfine]] electron states in that setup, <sup>2</sup>S<sub>1/2</sub> |F=0, m<sub>F</sub> = 0⟩ and |F = 1, m<sub>F</sub> = 0⟩, have very close energy levels, separated by 12.642831&nbsp;GHz. Ten [[Doppler cooling|Doppler-cooled]] ions were placed in a line 0.025&nbsp;mm long and coupled together. The researchers observed a subharmonic oscillation of the drive. The experiment showed "rigidity" of the time crystal, where the oscillation frequency remained unchanged even when the time crystal was perturbed. However, once the perturbation grew too strong, the time crystal "melted" and lost its oscillation.

Later in 2016, [[Mikhail Lukin]] at Harvard also reported the creation of a driven time crystal. His group used a [[diamond]] crystal doped with a high concentration of [[Nitrogen-vacancy center]]<nowiki/>s, which have strong dipole-dipole coupling and relatively long-lived spin [[Coherence (physics)#Quantum coherence|coherence]]. By driving this strongly-interacting dipolar spin system with microwave fields and reading out the ensemble spin state with an optical (laser) field, it was observed that the spin polarization evolved at half the frequency of the microwave drive. The oscillations persisted for over 100 cycles. This [[sub-harmonic]] response to the drive frequency is seen as a signature of time-crystalline order.

==Related concepts==
A similar idea called a choreographic crystal has been proposed.<ref>See {{harvp|Boyle et al.|2016}}</ref>

{{Portal bar|Physics|Science|Mathematics}}

==References==
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: {{cite journal|last1=Modi|first1=Kavan|last2=Brodutch|first2=Aharon|last3=Cable|first3=Hugo|last4=Paterek|first4=Tomasz|last5=Vedral|first5=Vlatko|title=The classical-quantum boundary for correlations: Discord and related measures|journal=Reviews of Modern Physics|volume=84|issue=4|year=2012|pages=1655–1707|issn=0034-6861|doi=10.1103/RevModPhys.84.1655|url=https://arxiv.org/pdf/1112.6238.pdf|arxiv=1112.6238|bibcode=2012RvMP...84.1655M|ref={{harvid|Modi et al.|2012}} }}
: {{cite journal|last1=Ray|first1=M. W.|last2=Ruokokoski|first2=E.|last3=Kandel|first3=S.|last4=Möttönen|first4=M.|last5=Hall|first5=D. S.|title=Observation of Dirac monopoles in a synthetic magnetic field|journal=Nature|volume=505|issue=7485|year=2014|pages=657–660|issn=0028-0836|doi=10.1038/nature12954|bibcode=2014Natur.505..657R|arxiv=1408.3133v1|url=https://arxiv.org/pdf/1408.3133v1.pdf|ref={{harvid|Ray et al.|2014}}|pmid=24476889}}
: {{cite journal|last1=Ray|first1=M. W.|last2=Ruokokoski|first2=E.|last3=Tiurev|first3=K.|last4=Mottonen|first4=M.|last5=Hall|first5=D. S.|title=Observation of isolated monopoles in a quantum field|journal=Science|volume=348|issue=6234|year=2015|pages=544–547|issn=0036-8075|doi=10.1126/science.1258289|bibcode=2015Sci...348..544R|url=https://aaltodoc.aalto.fi/bitstream/handle/123456789/16541/article5.pdf?sequence=8|ref={{harvid|Ray et al.|2015}} }}
: {{cite journal|last1=Reimann|first1=Peter|last2=Grifoni|first2=Milena|last3=Hänggi|first3=Peter|title=Quantum Ratchets|journal=Physical Review Letters|volume=79|issue=1|year=1997|pages=10–13|issn=0031-9007|doi=10.1103/PhysRevLett.79.10|url=https://pdfs.semanticscholar.org/eb04/b17564b443e5bcb7d9b8f579bbfb501db507.pdf|bibcode=1997PhRvL..79...10R|ref={{harvid|Reimann et al.|1997}} }}
: {{cite journal|last1=Roßnagel|first1=J.|last2=Abah|first2=O.|last3=Schmidt-Kaler|first3=F.|last4=Singer|first4=K.|last5=Lutz|first5=E.|title=Nanoscale Heat Engine Beyond the Carnot Limit|journal=Physical Review Letters|volume=112|issue=3|year=2014|issn=0031-9007|doi=10.1103/PhysRevLett.112.030602|url=https://arxiv.org/pdf/1308.5935.pdf|arxiv=1308.5935|bibcode=2014PhRvL.112c0602R|ref={{harvid|Roßnagel et al.|2014}}|pmid=24484127|page=030602}}
: {{cite journal|last1=Roßnagell|first1=J.|last2=Dawkins|first2=S. T.|last3=Tolazzi|first3=K. N.|last4=Abah|first4=O.|last5=Lutz|first5=E.|last6=Schmidt-Kaler|first6=F.|last7=Singer|first7=K.|title=A single-atom heat engine|journal=Science|volume=352|issue=6283|year=2016|pages=325–329|issn=0036-8075|doi=10.1126/science.aad6320|url=https://arxiv.org/pdf/1510.03681.pdf|arxiv=1510.03681|bibcode=2016Sci...352..325R|ref={{harvid|Roßnagel et al.|2016}} }}
: {{cite journal|last1=Tatara|first1=Gen|last2=Kikuchi|first2=Makoto|last3=Yukawa|first3=Satoshi|last4=Matsukawa|first4=Hiroshi|title=Dissipation Enhanced Asymmetric Transport in Quantum Ratchets|journal=Journal of the Physical Society of Japan|volume=67|issue=4|year=1998|pages=1090–1093|issn=0031-9015|doi=10.1143/JPSJ.67.1090|url=https://arxiv.org/pdf/cond-mat/9711045.pdf|arxiv=cond-mat/9711045|ref={{harvid|Tatara et al.|1998}} }}
: {{cite journal|last1=Volovik|first1=G. E.|title=On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order|journal=JETP Letters|volume=98|issue=8|year=2013|pages=491–495|issn=0021-3640|doi=10.1134/S0021364013210133|arxiv=1309.1845v2 |url=https://arxiv.org/pdf/1309.1845v2.pdf|bibcode=2013JETPL..98..491V}}
: {{cite journal|last1=von Keyserlingk|first1=C. W.|last2=Khemani|first2=Vedika|last3=Sondhi|first3=S. L.|title=Absolute stability and spatiotemporal long-range order in Floquet systems|journal=Physical Review B|volume=94|issue=8|year=2016|issn=2469-9950|doi=10.1103/PhysRevB.94.085112|arxiv=1605.00639v3|bibcode=2016PhRvB..94h5112V|url=https://arxiv.org/pdf/1605.00639v3.pdf|ref={{harvid|von Keyserlingk et al.|2016}} }}
: {{cite journal|last1=Wang|first1=Y. H.|last2=Steinberg|first2=H.|last3=Jarillo-Herrero|first3=P.|last4=Gedik|first4=N.|title=Observation of Floquet-Bloch States on the Surface of a Topological Insulator|journal=Science|volume=342|issue=6157|year=2013|pages=453–457|issn=0036-8075|doi=10.1126/science.1239834|arxiv=1310.7563v1|bibcode=2013Sci...342..453W|url=https://arxiv.org/pdf/1310.7563v1.pdf|ref={{harvid|Wang et al.|2013}} }}
: {{cite journal|last1=Watanabe|first1=Haruki|last2=Oshikawa|first2=Masaki|title=Absence of Quantum Time Crystals|journal=Physical Review Letters|volume=114|issue=25|year=2015|issn=0031-9007|doi=10.1103/PhysRevLett.114.251603|bibcode=2015PhRvL.114y1603W|arxiv=1410.2143v3|url=https://arxiv.org/pdf/1410.2143v3.pdf|pmid=26197119|page=251603}}
: {{cite journal|last1=Wilczek|first1=Frank|title=Quantum Time Crystals|journal=Physical Review Letters|volume=109|issue=16|year=2012|issn=0031-9007|doi=10.1103/PhysRevLett.109.160401|arxiv=1202.2539v2|url=https://arxiv.org/pdf/1202.2539v2.pdf|bibcode=2012PhRvL.109p0401W}}
: {{cite journal|last1=Wilczek|first1=Frank|title=Wilczek Reply:|journal=Physical Review Letters|volume=110|issue=11|year=2013a|issn=0031-9007|doi=10.1103/PhysRevLett.110.118902|url=http://xa.yimg.com/kq/groups/2385221/2027721577/name/WilzcekreplyPhysRevLett.110.118902-1.pdf|bibcode=2013PhRvL.110k8902W}}
: {{cite journal|last1=Wilczek|first1=Frank|title=Superfluidity and Space-Time Translation Symmetry Breaking|journal=Physical Review Letters|volume=111|issue=25|year=2013b|issn=0031-9007|doi=10.1103/PhysRevLett.111.250402|bibcode=2013PhRvL.111y0402W|arxiv=1308.5949v1|url=https://arxiv.org/pdf/1308.5949v1.pdf}}
: {{cite journal|last1=Willett|first1=R. L.|last2=Nayak|first2=C.|last3=Shtengel|first3=K.|last4=Pfeiffer|first4=L. N.|last5=West|first5=K. W.|title=Magnetic-Field-Tuned Aharonov-Bohm Oscillations and Evidence for Non-Abelian Anyons atν=5/2|journal=Physical Review Letters|volume=111|issue=18|year=2013|issn=0031-9007|doi=10.1103/PhysRevLett.111.186401|bibcode=2013PhRvL.111r6401W|arxiv=1301.2639v1|url=https://arxiv.org/pdf/1301.2639v1.pdf|ref={{harvid|Willett et al.|2013}} }}
: {{cite journal|last1=Yao|first1=N. Y.|last2=Potter|first2=A. C.|last3=Potirniche|first3=I.-D.|last4=Vishwanath|first4=A.|title=Discrete Time Crystals: Rigidity, Criticality, and Realizations|journal=Physical Review Letters|volume=118|issue=3|year=2017|issn=0031-9007|doi=10.1103/PhysRevLett.118.030401|arxiv=1608.02589v2|url=https://arxiv.org/pdf/1608.02589v2.pdf|bibcode=2017PhRvL.118c0401Y|ref={{harvid|Yao et al.|2017}} }}
: {{cite journal|last1=Yoshii|first1=Ryosuke|last2=Takada|first2=Satoshi|last3=Tsuchiya|first3=Shunji|last4=Marmorini|first4=Giacomo|last5=Hayakawa|first5=Hisao|last6=Nitta|first6=Muneto|title=Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions|journal=Physical Review B|volume=92|issue=22|year=2015|issn=1098-0121|doi=10.1103/PhysRevB.92.224512|arxiv=1404.3519v2|url=https://arxiv.org/pdf/1404.3519v2.pdf|bibcode=2015PhRvB..92v4512Y|ref={{harvid|Yoshii et al.|2015}} }}
: {{cite journal|last1=Yukawa|first1=Satoshi|last2=Kikuchi|first2=Macoto|last3=Tatara|first3=Gen|last4=Matsukawa|first4=Hiroshi|title=Quantum Ratchets|journal=Journal of the Physical Society of Japan|volume=66|issue=10|year=1997|pages=2953–2956|issn=0031-9015|doi=10.1143/JPSJ.66.2953|url=https://arxiv.org/pdf/cond-mat/9706222.pdf|arxiv=cond-mat/9706222|bibcode=1997JPSJ...66.2953Y|ref={{harvid|Yukawa et al.|1997}} }}
: {{cite journal|last1=Yukawa|first1=Satoshi|title=A Quantum Analogue of the Jarzynski Equality|journal=Journal of the Physical Society of Japan|volume=69|issue=8|year=2000|pages=2367–2370|issn=0031-9015|doi=10.1143/JPSJ.69.2367|url=https://arxiv.org/pdf/cond-mat/0007456.pdf|arxiv=cond-mat/0007456|bibcode=2000JPSJ...69.2367Y}}
: {{cite journal|last1=Zel'Dovich|first1=Y. B.|title=The quasienergy of a quantum-mechanical system subjected to a periodic action|journal=Soviet Physics JETP|date=1967|volume=24|issue=5|pages=1006–1008|url=http://jetp.ac.ru/cgi-bin/dn/e_024_05_1006.pdf|bibcode=1967JETP...24.1006Z}}
: {{cite journal|last1=Zhang|first1=J.|last2=Hess|first2=P. W.|last3=Kyprianidis|first3=A.|last4=Becker|first4=P.|last5=Lee|first5=A.|last6=Smith|first6=J.|last7=Pagano|first7=G.|last8=Potirniche|first8=I.-D.|last9=Potter|first9=A. C.|last10=Vishwanath|first10=A.|last11=Yao|first11=N. Y.|last12=Monroe|first12=C.|title=Observation of a Discrete Time Crystal|url=https://arxiv.org/pdf/1609.08684v1.pdf|arxiv=1609.08684v1|bibcode=2017Natur.543..217Z|journal=Nature|volume=543|issue=7644|year=2017|pages=217–220|issn=0028-0836|doi=10.1038/nature21413|ref={{harvid|Zhang et al.|2017}} }}
{{refend}}

===Books===
{{Refbegin|30em|indent=yes}}
: {{cite journal|last1=Bordag|first1=M.|last2=Mohideen|first2=U.|last3=Mostepanenko|first3=V.M.|title=New developments in the Casimir effect|journal=Physics Reports|volume=353|issue=1–3|year=2001|pages=1–205|issn=0370-1573|doi=10.1016/S0370-1573(01)00015-1|arxiv=quant-ph/0106045|url=https://arxiv.org/pdf/quant-ph/0106045v1.pdf}}
: {{cite book|last1=Bordag|first1=M.|last2=Mohideen|first2=U.|last3=Mostepanenko|first3=V.M.|last4=Klimchitskaya|first4=G. L|title=Advances in the Casimir Effect|url=https://books.google.com/books?id=CqE1f_s5PgYC|date=28 May 2009|publisher=Oxford University Press|location=Oxford|isbn=978-0-19-157988-2}}
: {{cite book|last1=Cao|first1=Tian Yu|title=Conceptual Foundations of Quantum Field Theory|url=https://books.google.co.uk/books?id=d0wS0EJHZ3MC&printsec=frontcover#v=onepage&q&f=falseC|date=25 March 2004|publisher=Cambridge University Press|isbn=978-0-521-60272-3|location=Cambridge}}
: {{cite book|last1=Enz|first1=Charles P.|editor1-last=Enz|editor1-first=C. P.|editor2-last=Mehra|editor2-first=J.|title=Physical Reality and Mathematical Description|chapter=Is the Zero-Point Energy Real?|date=1974|publisher=D. Reidel Publishing Company|location=Dordrecht|isbn=978-94-010-2274-3|pages=124–132|doi=10.1007/978-94-010-2274-3_8}}
: {{cite book|last1=Greiner|first1=Walter|last2=Müller|first2=B.|last3=Rafelski|first3=J.|title=Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics|date=2012|publisher=Springer|isbn=978-3-642-82274-2|doi=10.1007/978-3-642-82272-8|url=https://books.google.co.uk/books?id=Wh3-CAAAQBAJ&printsec=frontcover#v=onepage&q&f=false|ref={{harvid|Greiner et al.|2012}} }}
: {{cite book|last1=Lee|first1=T. D.|title=Particle Physics|url=https://books.google.co.uk/books?id=sZxBBAAAQBAJ&printsec=frontcover&vq=unobservable#v=onepage&q&f=false|date=15 August 1981|publisher=CRC Press|isbn=978-3-7186-0033-5}}
: {{cite book|last1=Feng|first1=Duan|last2=Jin|first2=Guojun|title=Introduction to Condensed Matter Physics|url=https://books.google.co.uk/books?id=-iuYN5arHwoC&printsec=frontcover#v=onepage&q&f=false|year=2005|publisher=World Scientific|location=singapore|isbn=978-981-238-711-0}}
: {{cite book|last1=Milonni|first1=Peter W.|authorlink1=Peter W. Milonni||title=The Quantum Vacuum: An Introduction to Quantum Electrodynamics|date=1994|publisher=Academic Press|location=London|isbn=978-0-124-98080-8|url=https://books.google.com/books?id=uPHJCgAAQBAJ&lpg=PP1&dq=inauthor%3A%22Peter%20W.%20Milonni%22&pg=PP1#v=onepage&q&f=false}}
: {{cite book|title=Quantum Mechanics for Pedestrians 2: Applications and Extensions|url=https://books.google.co.uk/books?id=KOy5BAAAQBAJ&printsec=frontcover#v=onepage&q&f=false|publisher=Springer|isbn=978-3-319-00813-4|last1=Pade|first1=Jochen|year=2014|issn=2192-4791|doi=10.1007/978-3-319-00813-4|location=Dordrecht}}
: {{cite book|last1=Schwinger|first1=Julian|title=Particles, Sources, And Fields, Volume 1: v. 1 (Advanced Books Classics)|date=1998a|publisher=Perseus|isbn=978-0-738-20053-8}}
: {{cite book|last1=Schwinger|first1=Julian|title=Particles, Sources, And Fields, Volume 2: v. 2 (Advanced Books Classics)|date=1998b|publisher=Perseus|isbn=978-0-738-20054-5}}
: {{cite book|last1=Schwinger|first1=Julian|title=Particles, Sources, And Fields, Volume 3: v. 3 (Advanced Books Classics)|date=1998c|publisher=Perseus|isbn=978-0-738-20055-2}}
: {{cite book|last1=Sólyom|first1=Jenö|title=Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics|url=https://books.google.com/books?id=zn-se2TKv3QC|date=19 September 2007|publisher=Springer|isbn=978-3-540-72600-5}}
: {{cite book|last1=Wilczek|first1=Frank|title=A Beautiful Question: Finding Nature's Deep Design|url=https://books.google.co.uk/books?id=Oh3ICAAAQBAJ&printsec=frontcover#v=onepage&q&f=false|date=16 July 2015|publisher=Penguin Books Limited|isbn=978-1-84614-702-9}}
{{refend}}

===Press===
{{Refbegin|30em|indent=yes}}
: {{cite web|author1=Aalto University|title=Physicists discover quantum-mechanical monopoles|url=https://phys.org/news/2015-04-physicists-quantum-mechanical-monopoles.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/PYXDV|archivedate=30 Apr 2015|date=30 April 2015}}
: {{cite journal|last1=Aitchison|first1=Ian|title=Observing the Unobservable|journal=New Scientist|date=19 November 1981|volume=92|issue=1280|pages=540–541|url=https://books.google.co.uk/books?id=riW31Fy4kpkC&printsec=frontcover#v=onepage&q&f=false|issn=0262-4079}}
: {{cite web|author1=Amherst College|title=Physicists create synthetic magnetic monopole predicted more than 80 years ago|url=https://phys.org/news/2014-01-physicists-synthetic-magnetic-monopole-years.html|archiveurl=http://archive.is/u1dh8|archivedate=29 Jan 2014|date=29 January 2014|website=phys.org|publisher=Science X}}
: {{cite web|last1=Aron|first1=Jacob|title=Computer that could outlive the universe a step closer|url=https://www.newscientist.com/article/dn22028-computer-that-could-outlive-the-universe-a-step-closer/|website=newscientist.com|publisher=New Scientist|archiveurl=http://archive.is/Z6d1F|archivedate=2 Feb 2017|date=6 July 2012}}
: {{cite web|last1=Ball|first1=Philip|title=Focus: New Crystal Type is Always in Motion|url=http://physics.aps.org/articles/v9/4|website=physics.aps.org|publisher=APS Physics|archiveurl=http://archive.is/HxWE0|archivedate=3 Feb 2017|date=8 January 2016}}
: {{cite journal|last1=Ball|first1=Philip|title=Scepticism greets pitch to detect dark energy in the lab|url=http://www.readcube.com/articles/10.1038/430126b|journal=Nature|volume=430|issue=6996|date=8 July 2004|pages=126–126|issn=0028-0836|doi=10.1038/430126b|bibcode=2004Natur.430..126B}}
: {{cite web|last1=Cartlidge|first1=Edwin|title=Scientists build heat engine from a single atom|url=http://www.sciencemag.org/news/2015/10/scientists-build-heat-engine-single-atom|website=sciencemag.org|publisher=Science Magazine|archiveurl=http://archive.is/0F5Oc|archivedate=1 Feb 2017|date=21 October 2015}}
: {{cite web|last1=Chandler|first1=David|title=Topological insulators: Persuading light to mix it up with matter|url=https://phys.org/news/2013-10-topological-insulators.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/9Ci5y|archivedate=8 Feb 2017|date=24 October 2014}}
: {{cite journal|last1=Coleman|first1=Piers|title=Quantum physics: Time crystals|journal=Nature|volume=493|issue=7431|date=9 January 2013|pages=166–167|issn=0028-0836|doi=10.1038/493166a|bibcode=2013Natur.493..166C}}
: {{cite web|last1=Cowen|first1=Ron|title="Time Crystals" Could Be a Legitimate Form of Perpetual Motion|url=https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/|website=scientificamerican.com|publisher=Scientific American|archiveurl=http://archive.is/UZYQA|archivedate=2 Feb 2017|date=27 February 2012}}
: {{cite web|last1=Daghofer|first1=Maria|title=Viewpoint: Toward Fractional Quantum Hall Physics with Cold Atoms|url=http://physics.aps.org/articles/v6/49#c2|website=physics.aps.org|publisher=APS Physics|archiveurl=http://archive.is/1Kztv|archivedate=7 Feb 2017|date=29 April 2013}}
: {{cite journal|last1=Gibney|first1=Elizabeth|title=The quest to crystallize time|journal=Nature|volume=543|issue=7644|year=2017|pages=164–166|issn=0028-0836|doi=10.1038/543164a|url=http://www.nature.com/news/the-quest-to-crystallize-time-1.21595|archiveurl=http://archive.is/WRq8v|archivedate=13 Mar 2017}}
: {{cite web|last1=Grossman|first1=Lisa|title=Death-defying time crystal could outlast the universe|url=https://www.newscientist.com/article/mg21328484-000-death-defying-time-crystal-could-outlast-the-universe/|website=newscientist.com|publisher=New Scientist|archiveurl=http://archive.is/2LeIF|archivedate=2 Feb 2017|date=18 January 2012}}
: {{cite web|last1=Hackett|first1=Jennifer|title=Curious Crystal Dances for Its Symmetry|url=https://www.scientificamerican.com/article/curious-crystal-dances-for-its-symmetry/|website=scientificamerican.com|publisher=Scientific American|archiveurl=http://archive.is/jDkID#selection-515.0-515.16|archivedate=3 Feb 2017|date=22 February 2016}}
: {{cite web|last1=Hewitt|first1=John|title=Creating time crystals with a rotating ion ring|url=https://phys.org/news/2013-05-crystals-rotating-ion.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/NORiD|archivedate=4 Jul 2013|date=3 May 2013}}
: {{cite web|last1=Johnston|first1=Hamish|title='Choreographic crystals' have all the right moves|url=http://physicsworld.com/cws/article/news/2016/jan/18/choreographic-crystals-have-all-the-right-moves|website=physicsworld.com|publisher=Institute of Physics|archiveurl=http://archive.is/zMle4#selection-1141.128-1141.346|archivedate=3 Feb 2017|date=18 January 2016}}
: {{cite web|author1=Johannes Gutenberg Universitaet Mainz|title=Prototype of single ion heat engine created|url=https://www.sciencedaily.com/releases/2014/02/140203101031.htm|website=sciencedaily.com|publisher=ScienceDaily|archiveurl=http://archive.is/iLS4K|archivedate=1 Feb 2017|date=3 February 2014|ref={{harvid|Johannes Gutenberg Universitaet Mainz|2014}} }}
: {{cite web|author1=Joint Quantum Institute|title=Floquet Topological Insulators|url=http://jqi.umd.edu/news/floquet-topological-insulators|website=jqi.umd.edu|publisher=Joint Quantum Institute|date=22 March 2011}}
: {{cite web|last1=Morgan|first1=James|title=Elusive magnetic 'monopole' seen in quantum system|url=http://www.bbc.co.uk/news/science-environment-25946734|website=bbc.co.uk|publisher=BBC|archiveurl=http://archive.is/kgRc6|archivedate=30 Jan 2014|date=30 January 2014}}
: {{cite web|last1=Moskowitz|first1=Clara|title=New Particle Is Both Matter and Antimatter|url=https://www.scientificamerican.com/article/majorana-particle-matter-and-antimatter/|website=scientificamerican.com|publisher=Scientific American|archiveurl=http://archive.is/GtTwC|archivedate=9 Oct 2014|date=2 October 2014}}
: {{cite web|last1=Ouellette|first1=Jennifer|title=World’s first time crystals cooked up using new recipe|url=https://www.newscientist.com/article/2119804-worlds-first-time-crystals-cooked-up-using-new-recipe/|website=newscientist.com|publisher=New Scientist|archiveurl=http://archive.is/vUMuu|archivedate=1 Feb 2017|date=31 January 2017}}
: {{cite news|last1=Pilkington|first1=Mark|title=Zero point energy|url=https://www.theguardian.com/education/2003/jul/17/research.highereducation|publisher=The Guardian|date=17 July 2003|archiveurl=http://archive.is/56vqz|archivedate=7 Feb 2017|website=theguardian.com}}
: {{cite journal|last1=Powell|first1=Devin|title=Can matter cycle through shapes eternally?|journal=Nature|year=2013|issn=1476-4687|doi=10.1038/nature.2013.13657|url=http://www.nature.com/news/can-matter-cycle-through-shapes-eternally-1.13657|archiveurl=http://archive.is/SOPK8|archivedate=3 Feb 2017}}
: {{cite web|last1=Rao|first1=Achintya|title=BaBar makes first direct measurement of time-reversal violation|url=http://physicsworld.com/cws/article/news/2012/nov/21/babar-makes-first-direct-measurement-of-time-reversal-violation|website=physicsworld.com|publisher=Institute of Physics|archiveurl=http://archive.is/FF0fG|archivedate=24 Mar 2015|date=21 November 2012}}
: {{cite web|last1=Richerme|first1=Phil|title=Viewpoint: How to Create a Time Crystal|url=http://physics.aps.org/articles/v10/5|website=physics.aps.org|publisher=APS Physics|archiveurl=http://archive.is/eXKGV|archivedate=2 Feb 2017|date=18 January 2017|ref={{harvid|Richerme|2017}} }}
: {{cite web|last1=Thomas|first1=Jessica|title=Notes from the Editors: The Aftermath of a Controversial Idea|url=http://physics.aps.org/articles/v6/31|website=physics.aps.org|publisher=APS Physics|archiveurl=http://archive.is/5CBHl|archivedate=2 Feb 2017|date=15 March 2013}}
: {{cite journal|last1=Qi|first1=Xiao-Liang|last2=Zhang|first2=Shou-Cheng|title=The quantum spin Hall effect and topological insulators|journal=Physics Today|volume=63|issue=1|year=2010|pages=33–38|issn=0031-9228|doi=10.1063/1.3293411|url=http://web.physics.ucsb.edu/~phys123B/w2015/QiZhangReview-1.pdf}}
: {{cite web|author1=University of California, Berkeley|title=Physicists unveil new form of matter—time crystals|url=https://phys.org/news/2017-01-physicists-unveil-mattertime-crystals.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/hc5GB|archivedate=28 Jan 2017|date=26 January 2017}}
: {{cite web|last1=Weiner|first1=Sophie|title=Scientists Create A New Kind Of Matter: Time Crystals|url=http://www.popularmechanics.com/science/a24957/time-crystals/|website=popularmechanics.com|publisher=Popular mechanics|archiveurl=http://archive.is/jpcXR|archivedate=3 Feb 2017|date=28 January 2017}}
: {{cite web|last1=Wolchover|first1=Natalie|title=Perpetual Motion Test Could Amend Theory of Time|url=https://www.quantamagazine.org/20130425-perpetual-motion-test-could-amend-theory-of-time/#|website=quantamagazine.org|publisher=Simons Foundation|archiveurl=http://archive.is/FubVX|archivedate=2 Feb 2017|date=25 April 2013}}
: {{cite web|last1=Wolchover|first1=Natalie|title=Forging a Qubit to Rule Them All|url=https://www.quantamagazine.org/20140515-forging-a-qubit-to-rule-them-all/|website=quantamagazine.org|publisher=Simmons Foundation|archiveurl=http://archive.is/15gEj|archivedate=15 Mar 2016|date=15 May 2014}}
: {{cite web|last1=Wood|first1=Charlie|title=Time crystals realize new order of space-time|url=http://www.csmonitor.com/Science/2017/0131/Time-crystals-realize-new-order-of-space-time|website=csmonitor.com|publisher=Christian Science Monitor|archiveurl=http://archive.is/xwzMc|archivedate=2 Feb 2017|date=31 January 2017}}
: {{cite web|last1=Yirka|first1=Bob|title=Physics team proposes a way to create an actual space-time crystal|url=https://phys.org/news/2012-07-physics-team-actual-space-time-crystal.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/5AuCp#selection-789.0-789.12|archivedate=15 Apr 2013|date=9 July 2012}}
: {{cite web|last1=Zakrzewski|first1=Jakub|title=Viewpoint: Crystals of Time|url=http://physics.aps.org/articles/v5/116|website=physics.aps.org|publisher=APS Physics|archiveurl=http://archive.is/f8aFI|archivedate=2 Feb 2017|date=15 October 2012}}
:{{cite web|last1=Zeller|first1=Michael|title=Viewpoint: Particle Decays Point to an Arrow of Time|url=http://physics.aps.org/articles/v5/129|website=physics.aps.org|publisher=APS Physics|archiveurl=http://archive.is/MQ5Qn|archivedate=4 Feb 2017|date=19 November 2012}}
: {{cite web|last1=Zyga|first1=Lisa|title=Time crystals could behave almost like perpetual motion machines|url=https://phys.org/news/2012-02-crystals-perpetual-motion-machines.html#nRlv|website=phys.org|publisher=Science X|archiveurl=http://archive.is/rjBZs|archivedate=3 Feb 2017|date=20 February 2012}}
: {{cite web|last1=Zyga|first1=Lisa|title=Physicist proves impossibility of quantum time crystals|url=https://phys.org/news/2013-08-physicist-impossibility-quantum-crystals.html|website=phys.org|publisher=Space X|archiveurl=http://archive.is/nZCdy|archivedate=3 Feb 2017|date=22 August 2013}}
: {{cite web|last1=Zyga|first1=Lisa|title=Nanoscale heat engine exceeds standard efficiency limit|url=https://phys.org/news/2014-01-nanoscale-standard-efficiency-limit.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/WZQfZ|archivedate=4 Apr 2015|date=27 January 2014}}
: {{cite web|last1=Zyga|first1=Lisa|title=Physicists propose new definition of time crystals—then prove such things don't exist|url=https://phys.org/news/2015-07-physicists-definition-crystalsthen-dont.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/k5Z8V|archivedate=9 Jul 2015|date=9 July 2015}}
: {{cite web|last1=Zyga|first1=Lisa|title=Time crystals might exist after all (Update)|url=https://phys.org/news/2016-09-crystals.html|website=phys.org|publisher=Science X|archiveurl=http://archive.is/g2i8V|archivedate=11 Sep 2016|date=9 September 2016}}
{{Refend}}

==External links==
{{colbegin|2}}
* [https://www.umdphysics.umd.edu/people/faculty/current/item/348-monroe.html Christopher Monroe bio, Maryland]
* [http://frankwilczek.com/ The Frank Wilczek website]
* [http://lukin.physics.harvard.edu/ Lukin Group, Harvard]
* [http://physics.berkeley.edu/people/faculty/norman-yao Norman Yao bio, Berkeley]
{{colend}}

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{{DEFAULTSORT:Condensed Matter Physics}}
[[:Category:Branches of thermodynamics]]
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